I actually read the exchange, she's not all wrong. Let me explain why I think that, before you rush to downvote, please try to address my arguments, and if you can't formulate a response that isn't an insult or an attack against me, maybe it's because it may be more accurate than you'd like.
Basically, she is saying that what makes the US the US is not the land, and that the "American" nation as we all know today has been built by European settlers, based on European ideas, with European cultural values and political institutions. She's pretty much 100% right in this. American Indians didn't build "America" so much as America happened to them. The roads, the cities, the economy, the culture of America, all of these have been built by the American nation founded by European settlers and into which various peoples have immigrated into. The European settlers who came here long ago cannot be called immigrants, because they didn't seek to integrate an existing nation, they were staking claims on land and building a new nation there, competing for space with the First Nations that were already there, eventually conquering their lands.
So I guess she doesn't like the term "Native American" because she feels it is a misnomer. The First Nations were not "American" before the settlers came because the nation known as "America" didn't exist yet. A nation is not a piece of land, it is first and foremost a people. Even today, many First Nations live in semi-autonomous reserves and are not wholly part of the United States of America.
Furthermore, "native" by definition only means someone who is born in a place. As such, everyone born in the United States currently is a native American, hence why people who oppose immigration are accused of "nativism" (a preference for native residents and discrimination against immigrants). Trump has been accused of being a "nativist" many times. How many people think that what is meant by that is that he is prejudiced in FAVOR of "Native Americans"?
So as such, the term "Native American" to indicate the descendants of the nations that were there before European colonization is certainly confusing. All people born in America are native of America, and the First Nations have not historically been part of the American nation. Indian is even worse. There seems to be no term that is technically correct to describe them. In French, we use the term "Amérindien", Amerindian, which is still rooted in inaccuracies, but at least it's a wholly new term that gives First Nations a descriptive term for themselves.